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Portfolio Selection – A Technical Note

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  • Ana Paula Martins

Abstract

This note develops the solutions of the static portfolio optimization problem in explicit matrix form. Three cases are contemplated and connected, with the derivation of relevant corner solutions: the unconstrained problem in the presence of risky assets only, the constrained one, and the presence of a risk-free asset. The use of a generalized form for the budget constraint allows us to use the structure to study the behavior of a complete borrower – subject or not to liquidity constraints – and infer the price of pure risk. Some properties of the several solutions are highlighted. The rationale for a linear relation between the standard deviation and the expected return of the unitary application in an efficient portfolio is derived. Requirements for useful existence in the market of any given security are established. Additionally, we infer the expected co-movement properties of efficient and the global market – or any other – portfolio.

Suggested Citation

  • Ana Paula Martins, 2012. "Portfolio Selection – A Technical Note," EERI Research Paper Series EERI_RP_2012_17, Economics and Econometrics Research Institute (EERI), Brussels.
    • Handle: RePEc:eei:rpaper:eeri_rp_2012_17
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    File URL: http://www.eeri.eu/documents/wp/EERI_RP_2012_17.pdf
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    Cited by:

    1. William H. Greene & Ana P. Martins, 2002. "Striking Features of the Labor Market," EERI Research Paper Series EERI RP 2002/08, Economics and Econometrics Research Institute (EERI), Brussels.
    2. William H. Greene & Ana P. Martins, 2013. "Striking Features of the Labor Market: Theory," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 56(2), pages 1-24.
    3. William H. Greene & Ana P. Martins, 2013. "Striking Features of the Labor Market: Empirical Evidence," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 56(2), pages 25-53.

    More about this item

    Keywords

    Portfolio choice; Mean Variance; CAPM; Quadratic Programming; Price of Risk.;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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